Timeline for $f(x)$ is irreducible but $f(x^n)$ is reducible
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
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| Aug 26, 2014 at 0:04 | comment | added | YCor | incidentally this shows that if $f$ (any monic irreducible polynomial) is cyclotomic , then $f(X^p)$ is reducible for all but finitely many primes $p$, while if $f$ is not cyclotomic (and $\neq X$), then $f(X^p)$ is irreducible for all but finitely many primes $p$. | |
| Aug 25, 2014 at 20:48 | comment | added | YCor | Very nice. It also works for degree 1 polynomials if we exclude multiples of $x$ and $x-1$. | |
| Aug 25, 2014 at 20:05 | history | answered | Vesselin Dimitrov | CC BY-SA 3.0 |